Modi, who earlier in the day met Iranian President Hassan Rouhani and an Indian business delegation, arrived at the huge venue where the leaders of Brazil, Russia, India, China and South Africa are to meet.
The five BRICS countries represent almost three billion people, or approximately 40 percent of the world population and have a combined GDP of $16.039 trillion, or 20 percent of the gross world product.
Russia's Bashkortostan republic is hosting the seventh BRICS summit and the 15th Shanghai Cooperation Organization (SCO) summit in capital Ufa where around 10,000 visitors are expected during the two back-to-back summits.
The BRICS summit is set to formalize the $100 billion BRICS New Development Bank and a currency reserve pool worth another $100 billion.
Russia assumed the BRICS rotating leadership in April 2015.
India and Pakistan are expected to be made permanent members of the China-led SCO.